Method for analyzing a gas sample

ABSTRACT

A method for determining the quantity and identity of an electrochemically convertible substance in a gas sample. The substance is converted in an electrochemical sensor producing an electrical output. The characteristic parameters of a curve-defining equation y(t)=k×(e −axt −e −bxt ) are calculated based on three measurements of output at times t, 2 t  and 4 t.  The integral under all or part of the curve is calculated to determine the quantity of the substance. The equation parameters are compared with standard values to determine the identity of the substance.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to a method for quantifying and identifying an electrochermically convertible substance in a gas sample. More specifically, the invention relates to a method for determining breath alcohol content quantitatively and for distinguishing and identifying other electrochemically convertible substances.

[0003] 2. Description of the Prior Art

[0004] Handheld breath alcohol testing devices have proved useful in roadside estimation of blood alcohol level of drivers. Electrochemical sensors are commonly used in these devices. In the typical arrangement, a sample of gas is introduced into the electrochemical sensor and a current is generated by the oxidation of the alcohol. The electrical output from the sensor increases from an initial value to a peak and then decreases back to at or near the initial value. These output amplitude measurements, plotted over time, form a curve hereafter referred to as the output curve. Electrochemical sensors exhibit some problems.

[0005] The first problem arises because errors in the measurement in breath alcohol content are introduced because the shape of the output curve is affected by variations in temperature, repeated use of the sensor, and aging of the sensor. In prior methods, the imprecision occurring due to the aforementioned variables, will alter the peak of the curve and, in turn, the measurement result.

[0006] A method disclosed in U.S. Pat. No. 4,770,026 attempts to overcome the dependencies of the output curve on these variables. In the known arrangement, the output measurements are summed to provide the integral of the entire output curve. This integral is the total area under the output curve and therefore represents the total current derived from the oxidation of the alcohol and therefore is proportional to the alcohol concentration in the sample. This method, however, requires the summation of the entire output curve without determining any curve fit function, making the measurement time prohibitively long.

[0007] A method of reducing this measurement time is disclosed in U.S. Pat. No. 5,393,495. This patent acknowledges the discovery that the amount of the reactant is proportional to the integral of the electrochemical sensor output curve. This method, however, finds the integral of a lognormal curve fit equation that approximates the sensor output curve. This method has the advantage that the integral for the lognormal curve can be calculated as soon as its equation is derived. This allows a shorter measurement time. The lognormal equation, being only a rough approximation of the output curve, yields the most accurate results only when it is based on a long measurement time and is less accurate when derived after a short time. The known method, therefore, still requires a long measurement time to achieve the highest accuracy.

[0008] Another problem with measuring alcohol in the breath is presented by the possibility of contaminants. While ethanol can be oxidized by the electrochemical sensor and produce an electrical output, so can other volatile substances such as methanol and isopropanol. The presence and oxidation of these contaminants changes the output curve and in turn the estimate of ethanol in the breath. A method is disclosed in U. S. Pat. No. 5,612,896 in which the areas under specific sections of the output curve are calculated and compared. The relationship of these areas gives an indication of the substances being reacted. This method requires that the output curve decline to at least 6% of its maximum value, thus requiring an extended measurement time, especially at low temperatures.

[0009] Porter, U.S. Pat. No. 5,458,853 is merely a two stage breathalyzer to save the cost of using a mouth piece for each test when it may not be necessary. Porter does disclose an exponential equation for a fuel cell's function similar to one disclosed, used and claimed herein. Porter's use of the equation is limited to transformation manipulation to isolate the reaction constant of the fuel cell and thus enable the preliminary test to detect the presence of alcohol.

[0010] The Porter apparatus and disclosure makes use of prior art methods of calculation and determination of breath analysis. Porter views the exponential equation as lacking stability and precision for calculation of alcohol.

OBJECTS OF THE INVENTION

[0011] It is the principal object of the present invention to provide an improved method of gas analysis which reduces the amount of time required for a measurement and improves the accuracy of measurement.

[0012] Another object of the invention is to provide a method of the foregoing character which facilitates identification of the reactants and reduces measurement errors.

[0013] Further objects and advantages of the invention will become apparent from a consideration of the drawings and ensuing description.

SUMMARY OF INVENTION

[0014] The method according to the invention includes the steps of: measuring the electrical output of an electrochemical sensor on a periodic basis, using these measurements to calculate an exponential fit equation that approximates the sensor output, integrating the equation to approximate the area under the output curve, and using the parameters of the equation to determine the type of substance being reacted.

[0015] The improvement of this method is based on the discovery of an equation that precisely matches the electrochemical sensor output curve and the characteristics of the reaction itself. The reaction and the discharge in the electrochemical sensor are exponential decay functions. The discovered exponential fit equation consists of multiple exponential parameters and a magnitude parameter. One of the exponential parameters in the equation represents the reaction. Another exponential parameter represents the discharge of the sensor. The exponential fit curve parameters are determined after a short amount of time and thus provide a fast and accurate quantification of reactant, independent of temperature, repeated testing, and sensor age. The curve parameters additionally allow identification of the reactant. As contemplated the curve fitting is based on a selected electrochemically reactive compound. The equation constants for that reactant are known and used as a standard against which the actual sample is compared. If there are contaminates or if the tested reactant differs from the target reactant, the equation fitting the actual results will differ from the standard equation, this may be by superposition of multiple curves due to a contaminate adding its curve fitting equation to the standard or targeted curve fitting equation. Thus in a particular sample, the curve fitting equation may not match the targeted reactant but may match other known reactants. Alternatively, the tested sample may have two or more exponential components with different constants representing the contribution of the two or more different reactants present in the sample and their different reaction constants and concurrently the two or more different constants for the discharge constants would be present as there would be concurrent multiple exponential components for the discharge component of the actual sample curve. A further advantage of this method is to test if the sample is contaminated by other types of reactants, and if not, then determine the total of the reactant and thus the quantity of the targeted reactant, i e. ethanol or other desired products.

[0016] The early determination of the exponential fit curve provides a quantification of the reacting substance before the entire output curve has been measured. The accuracy of the present invention is not compromised by an early measurement time because the present invention discloses an equation that very precisely matches the sensor output curve.

[0017] The present invention provides a precise calculation of the true reaction parameters at an early time in the reaction cycle yielding a faster and more accurate determination.

[0018] The equation disclosed is of the general form y(t)=k×(e^(−axt)−e^(−bxt)) where y(t) is the amplitude of the output curve at time t, k is the amplitude factor, b is the reaction factor, and a is the discharge factor. Three measurements are needed to solve for the three parameters; the first measurement is at any time (t) from the start of the curve, the second measurement at twice this time (2t) from the start of the curve, and the third measurement four times this time (4t) from the start of the curve. Solving the equation using these measurements yields the three factors; k, a, and b, and therefore, the characterization of the entire electrochemical sensor output curve.

[0019] Other useful results can be derived once the exponential fit curve equation has been determined:

[0020] (1) The total area under the exponential fit curve, and therefore the quantity of reactant, can be determined by integrating the exponential fit curve from zero to infinity.

[0021] (2) The area under any curve segment can be found by integrating the exponential fit equation between the time at the start of the segment and the time at the end of the segment.

[0022] (3) The area under any curve segments between given sensor output amplitudes can be found by using the using the exponential fit equation to solve for the times corresponding to the magnitudes and then integrating between these times.

[0023] (4) The time of the peak of the exponential fit curve can be determined by solving the first derivative of the exponential fit equation for zero.

[0024] (5) The peak measurement can be found by solving the exponential fit equation for the peak time.

[0025] (6) The inflection point of the exponential fit tail can be determined by solving the second derivative of the exponential fit equation for zero.

[0026] (7) The “b” factor is equivalent to the rate of reaction in the electrochemical sensor, and the “a” factor is equivalent to the rate of discharge. Different substances react at different rates and thus yield different “a” and “b” factors. Once these factors are determined they can be compared to characteristics of known reacting substances to determine the reactant type.

DESCRIPTION OF THE DRAWING

[0027]FIG. 1 is a block diagram showing the electronic circuit of a gas analysis apparatus embodying the present invention.

[0028]FIG. 2 is a chart showing output curves for trials described herein.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0029] Referring now to FIG. 1 showing apparatus incorporating an electronic circuit utilizing the method of the present invention, the microprocessor 20 reads the clock 21 and records the start time upon introduction of a gas sample into the electrochemical fuel cell sensor 22. The output 24 of the sensor 22 is amplified by an amplifier 25 and input to an analog to digital converter 26. At predefined periodic intervals after the start time the microprocessor 20 signals the analog to digital converter 26 and a measurement memory 28 to record a measurement. This signal causes the analog to digital converter 26 to latch the analog sensor output amplitude and causes the measurement memory 28 to read the digital representation of this amplitude, which may be a current or voltage value. The microprocessor reads measurements from the measurement memory 28, calculates the equation or curve parameters, calculates the quantity of reactant, and displays the result on the display 29. To this end, the microprocessor is programmed to solve the following equations according to the measurements.

[0030] I have discovered that the basic or principal equation utilizable by the microprocessor to produce the desired analytical results is y(t)=k×(e^(−axt)−e^(−bxt)), in which “b” represents the fuel cell reaction rate, “a” represents the fuel cell discharge rate, and “k” is the amplitude factor. This equation defines a curve that, starting at zero output and time rapidly reaches a peak output and then slowly declines over time toward a zero output at infinite time.

[0031] The equation factors or parameters k, a, and b, are calculated in the microprocessor by retrieving three sensor output measurements, one at time t; another at twice that time, 2t; and a third at four times that time, 4t. The following equations, derived from the basic equation, are used by the microprocessor to determine the parameters a, b, and k: $\begin{matrix} {a = {- \frac{\ln \left\lbrack {\left( {\frac{y_{2\quad t}}{y_{t}} + \sqrt{{{2*\frac{y_{4\quad t}}{y_{2\quad t}}} - \left( \frac{y_{2\quad t}}{y_{\quad t}} \right)^{2}}}} \right)/2} \right\rbrack}{t}}} \\ {b = {- \frac{\ln \left\lbrack {\left( {\frac{y_{2\quad t}}{y_{t}} - \sqrt{{{2*\frac{y_{4\quad t}}{y_{2\quad t}}} - \left( \frac{y_{2\quad t}}{y_{\quad t}} \right)^{2}}}} \right)/2} \right\rbrack}{t}}} \\ {k = \frac{y_{t}}{\sqrt{{{2*\frac{y_{4\quad t}}{y_{2\quad t}}} - \left( \frac{y_{2\quad t}}{y_{\quad t}} \right)^{2}}}}} \end{matrix}$

[0032] The area under exponential curve defined by the curve equation between any two times (t start and t stop) can be found by integrating the exponential equation between these times as limits. This integral is given by the equation: ${Area} = {k \times \left( {\frac{_{start}^{{- a} \times t}}{a} - \frac{_{start}^{{- b} \times t}}{b} - \frac{_{stop}^{{- a} \times t}}{a} - \frac{_{stop}^{{- b} \times t}}{b}} \right)}$

[0033] For the integration under the entire output curve of the equation(t start=0 and t stop=∞) the equation simplifies to: ${Area} = {k \times \left( {\frac{1}{a} - \frac{1}{b}} \right)}$

[0034] Other important information can be derived from these factors or rate and magnitude parameters. The peak time (t peak) can be found by solving the first derivative of the exponential fit equation for zero. This results in the following solution for the peak time: $t_{\quad {peak}} = \frac{\ln \left( {a/b} \right)}{a - b}$

[0035] The magnitude of the peak of the curve can be found by solving the exponential fit equation for t peak resulting in the following solution:

y _(peak)(t)=k×(e ^(−axt) _(peak) −e ^(−bxt) _(peak))

[0036] The a factor indicates the rate of discharge in the electrochemical sensor and the b factor indicates the rate of reaction. Because different substances will react and discharge at different rates the a and b factors can be used to identify the reactant. The following table shows the relationship of a, b, and t peak for isopropanol and methanol related to the values for ethanol: a b t peak Ethanol 1.00 1.00 1.00 Isopropanol 0.95 1.35 0.83 Methanol 0.49 0.44 2.20

[0037] In the preferred embodiment, ethanol reference values for a, b, and t peak are stored during a calibration procedure. After each test, a, b, and t peak are compared to the reference values. As shown in the table, isopropanol will produce a value for b that is 1.35 times the ethanol reference value and a t peak of 0.83 times the ethanol reference value. Methanol provides values for both a and b that are less than half the reference values and a t peak that is 2.2 times the reference value. Such a comparison to the ethanol reference allows an identification of the reactant.

[0038] Because the exponential parameter equations use sets of measurements at time t, 2t, and 4t, new parameters for the equation can be produced after every fourth measurement. The sequence of results can be averaged to provide the most precise results.

[0039] The area under the curve defined by the equation is directly proportional to the alcohol content of the gas sample. This area is determined by integrating, the equation, and applying a proportion factor to express the alcohol or other measured gas content of the gas sample.

[0040] Measurements of gas samples with known concentrations of ethanol corresponding to blood alcohol content (BAC) were made on the apparatus embodying the method of the present invention. For each such gas sample, the method produced the results shown in Table I. In this table, the first column (Gas Sample 1) is a calibration. These results are plotted as curves 1, 9, 3, 4, and 5 in the chart shown in FIG. 2. The results demonstrate the utility of the method embodying the present invention in accurately analyzing alcohol containing gas samples. TABLE I GAS SAMPLE 1 2 3 4 5 Known Alcohol Concentration in Gas Sample (BAC) 0.100 0.020 0.040 0.070 0.100 t 30 30 30 30 30 vt 131 31 65 116 162 v2t 121 25 54 96 136 v4t 73 13 28 49 71 a 0.0092 0.0112 0.0114 0.0117 0.0114 b 0.0601 0.0799 0.0704 0.0696 0.0684 k 220.3 49.7 110.4 200.1 278.1 alcohol 20319.2 3825 8095 14203 20396 Calibrate 203192 203192 203192 203192 203192 Factor Result 0.100 0.019 0.040 0.070 0.100 tpk 36.9 28.6 30.8 30.8 31.5 ypeak 131 31 65 116 162

[0041] The method disclosed with further known calculations by the microprocessor can be used to compare and determine the tested sample's reactant identification. The comparison of the tested sample's exponential fit equation constants with stored values of fit equation constants of different reactants can be done and the output will identify the reactant tested.

[0042] As an additional embodiment, the microprocessor may be programmed by common methods to determine if the tested reactant's curve is a superposition of two or more reactants curves. If so, further tests can be done to determine the ethanol alcohol content in the subject. Also, the microprocessor can calculate and compare the tested sample's curve and its deviation from the target reactant or reactants' curves. If it meets a predetermined level of what deviation is acceptable, then the microprocessor finishes the desired calculations and determines the values desired. 

1. A method of determining the quantity of an electrochemically convertible substance in a gas sample, the method comprising the steps of: (a) introducing said gas into an electrochemical sensor wherein said gas is electrochemically converted producing an electrical output; (b) measuring said output at three or more predetermined time intervals; (c) using said measurements to calculate the constants of a curve-defining equation with two or more exponential terms, each with constant factors a or b: (b) is the reaction factor and (a) is the discharge factor of the electrochemical sensors reaction with the reactant and (k) is an amplitude factor of the equation being of the general form, y(t)=k×(e^(−axt)−e^(−bxt)); and (d) determining the quantity of said substance be integrating tinder all or part of the curve defined by said equation.
 2. The method of claim 1 wherein the equation is integrated between times that are defined by output levels of the curve.
 3. The method of claim 1 wherein the equation is integrated between times that are defined by multiples of the peak time.
 4. The method of claim 1 wherein the equation is integrated between zero and infinite time.
 5. The method of claim 1 wherein the said substance is ethanol.
 6. The method of claim 1 wherein the constants in said equation are calculated using said measurements at time t, time 2t, and time 4t.
 7. A method of identifying an electrochemically convertible substance in a gas sample, the method comprising the steps of: (a) introducing said gas into an electrochemical sensor wherein said gas is electrochemically converted producing an electrical output; (b) measuring said output at three predetermined time intervals; (c) using said measurements to calculate the constants of a curve-defining equation with two or more exponential terms, each with constant factors a or b: (b) is the reaction factor and (a) is the discharge factor of the electrochemical sensors reaction with the reactant and (k) is an amplitude factor of the equation being of the general form, y(t)=k×(e^(−axt)−e^(−bxt)); (d) comparing the curve of the sample to the specimen curves of one or more selected reactants; and (e) determining if the sample contains one or more of the selected reactants or is contaminated by other reactants.
 8. The method of claim 7 wherein the said substance is an alcohol.
 9. The method of claim 7 wherein the said parameters are calculated using said measurements at time t, time 2t, and time 4t.
 10. A method of determining characteristic parameters of the electrochemical sensor output produced by the oxidation of an oxidizable substance in a gas when the output is represented by an equation of two or more exponential terms of the general form y(t)=k×(e^(−axt)−e^(−bxt)) where (b) is the reaction factor and (a) is the discharge factor and (k) is the amplitude factor said method comprising the steps of: (a) introducing said gas containing said oxidizable gas substance into said sensor wherein said substance is electrochemically converted producing an electrical output; (b) measuring said output at three predetermined time intervals; (c) using said measurements to calculate the constants of a curve-defining equation; and (d) using said measurements to calculate said characteristic parameters.
 11. The method of claim 10 wherein the said characteristic parameter is the time at which the curve defined by said equation peaks.
 12. The method of claim 10 wherein said characteristic parameter is the approximate fuel cell output level for a given time.
 13. The method of claim 10 wherein said characteristic parameter is the time at which the fuel cell reaches a given output level.
 14. The method of claim 10 wherein the said substance is ethanol.
 15. The method of claim 10 wherein the said characteristic parameters are calculated using said measurements at time t, time 2t, and time 4t.
 16. The method for expressing the output of a fuel cell sensor for analyzing an alcohol containing gas is a curve defining equation where (b) is the reactant factor and (a) is the discharge factor of the fuel cell and specific alcohol and (k) is the amplitude factor of a curve defining equation y(t)=k×(e^(−axt)−e^(−bxt)).
 17. A method of determining the alcohol content of a breath sample using a fuel cell apparatus which produces a varying current output over a period of time as a function of the alcohol content of said sample, and producing a reaction current as a function of time according to a curve-defining equation with two or more exponential terms, each with constant factors, the reaction factor (b) and the discharge factor (a) of the electrochemical sensor's reaction with the reactant and an amplitude factor (k) the equation being of the general form, y(t)=k×(e^(−axt)−e^(−bxt)); (a) feeding said sample to said fuel cell apparatus; (b) measuring and determining a current output from said apparatus at times t, 2t, and 4t; (c) calculating the parameters of said fuel cell using, said times and measured current outputs in said equation; and (d) integrating said equation thus defined to determine the area under a curve defined thereby, said area being proportionate to the alcohol content of said breath sample.
 18. A method of determining the alcohol content of a human breath comprising the steps of (a) using a sensor to oxidize a sample of said breath and produce an output current. (b) measuring said current at three times t, 2t, and 4t; and (c) using a computer to solve the equation y(t)=k×(e^(−axt)−e^(−bxt)) using said currents and times to determine the factors a, b, and k where (b) is the reaction rate and (a) is the discharge rate of the sensor's reaction with the alcohol and k is the amplitude factor in said equation; and (d) integrating said equation to determine the area thereunder between selected limits, said area being representative of said alcohol content.
 19. A method as defined in claim 18 wherein said limits of integration are 0 and infinity, and said integral is calculated according to the equation y(t)=k×(e^(−axt)−e^(−bxt)).
 20. A method of determining the quantity of an oxidizable substance in a gas sample comprising the steps of: (a) oxidizing in an electronic sensor a quantity of said substance present in said sample of said gas, said sensor producing measurable currents over periodic time intervals; (b) measuring said currents at three periodic time intervals t, 2t, 2nd 4t; (c) using said periodic current measurements to determine the factors a, b, and k of an oxidation equation y(t)=k×(e^(−axt)−e^(−bxt)) where (b) is the reaction factor of said sensor, (a) is the discharge factor of said sensor, and (k) is the amplitude factor; and (d) integrating said equation between defined limits to determine the area thereunder as a measure of the quantity of said substance in said sample within said defined limits.
 21. A method as defined in claim 20 wherein said oxidizable substance is an alcohol.
 22. A method as defined in claim 20 wherein said oxidizable substance is ethanol.
 23. A method as defined in claim 20 wherein said oxidizable substance is a mixture of alcohols. 